Improved Berezin-Li-Yau inequalities with a remainder term

Timo Weidl

Improved Berezin-Li-Yau inequalities with a remainder term

Spectral Theory 2007-12-03 v1 Mathematical Physics math.MP

Authors: Timo Weidl

Abstract

We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$ . It contains a correction term of the order of the standard second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains.

Keywords

laplacian eigenvalues dirichlet problem inequalities

Cite

@article{arxiv.0711.4925,
  title  = {Improved Berezin-Li-Yau inequalities with a remainder term},
  author = {Timo Weidl},
  journal= {arXiv preprint arXiv:0711.4925},
  year   = {2007}
}

Comments

Dedicated to M. Sh. Birman on the occasion of his 80th birthday

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